The pulse Doppler technique is common to most modern surveillance and tracking radars, and ultrasound systems. This technique employs a sequence of transmitted pulses which impinge on a target, are reflected from the target and are collected back in the receiver. This technique is particularly convenient when the velocity of the target is significantly different from the velocity of the background scatterers such as the ground, trees, foliage and so on. Under this condition, the detection capability of the system is maximized in terms of the signal to noise ratio (SNR) so that the probability of detection is improved.
Most modern surveillance radars scan the surrounding space using a relatively narrow radiation beam. The total scan time is usually the user specified parameter of the system. The fraction of scan time, allocated to collect target return from each beam direction, is called time-on-target. During this fraction of time a sequence of pulses is transmitted by the radar. The interval between the rise of any two consecutive pulses is called the PRI (Pulse Repetition Interval) and the rate of the pulses is called PRF (Pulse Repetition Frequency). Detection and measurement processes can be realized by using constant or variable PRF during the time-on-target interval. The maximum SNR can be achieved by coherent integration of all target returns during the entire time-on-target interval. Prima facie, the most tempting scheme for realization of such concept would appear to be to use a single constant pulse repetition frequency (PRF) for transmitting pulse sequence and utilization of target returns. However this scheme does not support unambiguous measurement of range or velocity or both.
Another problem related to a single PRF scheme of detection is the problem of blind zones (blind ranges and Doppler frequencies) in the detection map. This problem reflects the periodic nature of transmitting and receiving in pulse radar detection scheme and is known as the visibility problem.
One solution, known in the prior art, to both the ambiguity and the visibility problems is to transmit two or more pulse sequences consecutively, each sequence having a different PRF. Each sub-interval with constant PRF provides a different “scale” of ambiguous but simultaneous measurement of the target range and Doppler frequency. The combination of all measurements (each with a different PRF) during time-on-target interval allows ambiguity resolution, but requires independent attempts of detection. In other words, the requirement to provide simultaneous detection and measurement of the target leads to partitioning of the time-on-target interval to several independent sub-intervals, each of which represents a relatively small part of the entire time-on-target interval. The detection process in each sub-interval, known also as “Coherent Processing Interval” and for short CPI, can be performed optimally by using coherent integration, but the maximum energy collected from the target return is only a fraction of the entire energy that could be collected during the entire time-on-target interval. Any logical or arithmetical combination of the results of sub-interval leads to losses and degradation in probability of detection in comparison with coherent integration of the signal during entire time-on-target interval.
The concept of ambiguity resolution in range is presented in FIG. 1, showing the signals received when three pulse sequences shown respectively as PRF1, PRF2 and PRF3 are transmitted, each having a different PRF. The returned signals consist of a first pulse sequence 10 having a first PRI 11, a second pulse sequence 12 having a second PRI 13, and a third pulse sequence 14 having a third PRI 15. By using several frequencies, the unambiguous range can be solved. This is depicted in FIG. 1, where the unambiguous range 16 is detected at a position where pulses in the three pulse sequences coincide. Generally, the unambiguous range and Doppler of the target can be imagined as “coordinates” of the target detection hit of the unfolded range-Doppler map, which covers full range of the radar specified detection ranges and velocities (Doppler frequencies). This map is not explicitly represented in firmware or software of the radar, but one can think of it as sets of target hit coordinates, each for every detected target.
The narrow band signal that is collected in the receiver is usually modeled as s(t)=A(t)cos(2πfct+Φ(t))+N(t), where t is time, A is the amplitude, fc is the carrier frequency, Φ is the phase, and N is the noise. A basic assumption in this model is that the bandwidth of the amplitude A is orders of magnitude smaller than fc. The signal is processed along the receiving channel. It is frequency down-converted, filtered, split into two channels called the in-phase and quadrature, de-modulated (or pulse compressed) and digitized—not necessarily in that order. It is customary to represent the result obtained at this stage of the processing of a single PRF as a complex value entity: xkl=xl(tk)=Blej(Φl0+2πfdtk)+nl(tk), where l is the index of the PRF and is related to the time interval of the measurement, tk is the time of the specific sample, known as the “range gate” number, Bl is the amplitude which is constant within the period of the measurement, Φl0 is some phase constant within the period of the measurement, fd is the Doppler frequency, and nl is the complex noise.
FIG. 2 shows a prior art method for target detection in a pulse-Doppler coherent system using L different PRFs. As denoted by 20, a signal xnm(l)=x(l)(tnm) is received for each PRF used, where l=0 to L−1 is the PRF index, n is the pulse number in the signal, m is the range gate, and tn,m is the sampling time of the signal of the range gate m of the pulse n, and is given by tn,m(l)=nPRI(l)+mRG, where PRI is the pulse rate interval and RG is the duration of a single range gate. At 22, the signals Xnm(l) are subjected to coherent integration. This involves performing a discrete Fourier transform on the signals xnm(l) to generate a signal spectrum for each range gate m. The combination of all spectra for all range gates, obtained for each CPI, composes the folded range-Doppler map given by:
            X      km              (        ℓ        )              =                  ∑                  n          =          0                                      N                          (              l              )                                -          1                    ⁢                        x          nm                      (            l            )                          ⁢                  w          n                ⁢                  ⅇ                      -                                          2                ⁢                π                ⁢                                                                  ⁢                j                ⁢                                                                  ⁢                kn                            K                                            ,          ⁢      k    =    1    ,  …  ⁢          ,  K  ,      l    =    1    ,  …  ⁢          ,  L  ,      m    =    1    ,  …  ⁢          ,      M          (      l      )      where N(l) is the number of pulses in the signal, k is an index of the Doppler frequency, K is the number of Doppler frequencies, wn is a weighting factor, and M(l) is the number of range gates of the PRF 1. At 24, real-valued range-Doppler maps are generated for each PRF 1, a real-valued K by M(l) matrix P(l) is defined by setting, Pkm(l)=|Xkm(l)|2 for each pair of indices k and m, and at 26, the target detection is performed, whereby it is determined whether the value Pkm(l) is greater than or equal to a predetermined threshold T. If so, then at 28, Hkm(l) is set to 1. If not, then at 30, Hk,m(l) is set to 0. This defines a K×M(l) binary matrix H(l) for each value of l. This process is repeated for each CPI independently, producing the sets of target hits for each CPI, which are determined by their range—Doppler cell addresses—each PRF defines its own (generally folded) scale of cell addressing. Thereafter, the algorithm obviously need not record the matrices, but rather the sets of target hits and their cell coordinates. At 32, the hit sets for each PRF are unfolded by periodically increasing the cell addresses in range direction by a step of ambiguous range up to the maximum instrumental range and in Doppler direction by step of PRF up to the maximum Doppler frequency (the unfolded target hits for each PRF can be interpreted as non-zero values of some sparse matrices composed from zeros and ones)—the matrices Hl are subjected to a process known as “unfolding”. In this process, the dimensions of each matrix Hl are increased by defining Hk′,m′(l) for values of m′ for which Rmin<m′·RG<Rmax where [Rmin,Rmax] is a predetermined detection region of interest, and for values of k′ for which Dmin<k′·PRF/K<Dmax, Where [Dmin,Dmax] is a predetermined region of Doppler frequencies of interest, by setting Hk′m′(l)=Hkm(l), where k=k′ mod K, and m=m′ mod M. In step 34, the matrices Hl are resampled by defining, for each pair of indices k, m, new indices p and q, as follows. The range of interest is divided into subintervals of a predetermined length Δr. A value of p is found from among all allowed values of p (i.e. integral values of p for which 0≦pΔr≦Rmax−Rmin) such that Rp=Rmin+p·Δr is closest to the range represented by the range gate m. The interval [Dmin,Dmax] is divided into subintervals of a predetermined length Δd. A value of q is found from among all allowed values of q (i.e. integral values of q for which 0≦qΔd≦Dmax−Dmin) such that Dq=Dmin+q·Δd is closest to k. This generates at 36 new binary matrices Ul where Up,ql=Hk,ml, wherein the indices p,q correspond to the indices k,m. The sum A of the unfolded matrices is then calculated at 37, where
      A          p      ,      q        =            ∑              l        =        0                    L        -        1              ⁢                  U                  p          ,          q                l            .      At 38, it is determined, for each pair of indices, whether the sum Ap,q is greater than or equal to a predetermined threshold A. If so, then at 40 a target is detected at the location having the associated indices p,q, and the process terminates. If not, then at 42 it is determined that a target is not detected at the location having the associated indices p,q, and the process terminates.
To summarize, the following observations are made:
1. Although target coherency is maintained for all of the pulses transmitted within the time-on-target interval, in known methods, only the signal received within a single CPI is integrated coherently.
2. The effectiveness of the integration depends on the coherence of the signal. The notion of coherence means that the relative phases are constant within the period of the measurement (up to some relatively small noisy contribution) or they vary in a predictable manner. Normally this requirement implies that the radar contributes a phase and amplitude that are essentially constant, at least within the time of measurement, and that the contribution of the target to phase variation is mainly due to its motion. The greater the signal-to-noise ratio of a target, the greater is its maximal detection range. Thus, increasing the coherent integration interval to the whole period when a target is illuminated by the antenna (time-on-target interval), the maximum possible signal-to-noise ratio is obtained, and, as a result, the maximum detection range.
Although theoretically two PRFs are sufficient to resolve ambiguity, the required number of PRFs is actually higher. This is due to the fact that some range gates are blind in each PRF. In the simplified representation of FIG. 1, these are the ranges, corresponding to the time during which the system is transmitting and cannot receive. This was referred to above as the problem of visibility. The number of PRFs used typically varies from 2 to 8 depending on the level of visibility that is required. However, the amount of time that can be allocated to the integration procedure of each PRF is reduced as the number of PRFs is increased. Since the signal-to-noise ratio is proportional to the coherent integration interval duration, as the number of PRFs is increased, the signal to noise ratio of each PRF decreases. This impairs the effectiveness of the conventional technique.